32 bit programs will work in the 32 and 64 bit versions of win7 natively... just like they did with Vista... just like they did with winXP.
Click install, follow the instructions, it is fairly simple.
For larger software more and more stuff is beginning to have 64bit options, plus a 64bit OS allows for the use of more than 4GB of ram, so please do yourself a favor and get the 64bit version of win7 or win8 to future-proof yourself. Just about every processor made in the last 8 years can do 64bit just fine, so it should not be an issue.